The accurate estimation of ultimate claims is of vital importance for reinsurance companies in respect of the pricing and risk management. Among others, models like Chain Ladder or Cape Cod are widely used in practice. Disadvantages of these models are that information of each single loss is not fully taken into account, reinsurance contract features cannot be applied correctly, and an assumption about the ultimate loss distribution has to be done. Since current single loss development (SLD) models are not capable of overcoming these disadvantages, a new SLD model is developed based on real motor third party liability (MTPL) claims data. The available claims data is analysed for possible influential effects to answer the question of homogeneity for the market data. All single claims of the market dataset are considered as point cloud focusing on the incurred values, the payment ratio, and the related loss development factor (LDF). Hereby, the time component that is usually considered for most of the aggregated and SLD models is implicitly covered by these parameters. For this point cloud as new model framework, a cluster analysis is performed to find similar groups for a later development. Based on each cluster, the related developments are then modelled by a grid-type or Bernstein copula and restricted by two conditions. The first condition is limiting the maximal possible LDF with an LDF surface while the second condition is focusing on the jump pattern, e.g. the historical development path of a claim, to improve the future developments. A next development step of a single claim is then drawn from the respective copula under these two conditions resulting in the new copula-based SLD model. For the evaluation, several tests with respect to the runtime, number of simulations, and plausibility are done. Furthermore, the copula-based SLD model is applied to real MTPL claims data provided by a leading reinsurer. Hereby, a comparison of the results with the Chain Ladder model, Munich Chain Ladder model, and Cape Cod model is done. Moreover, a backtesting is performed to compare the simulated and original ultimate loss distribution which is of major importance for reinsurance pricing. Hereby, the copula-based SLD model is applied to the German MTPL market for which the impact of each model component is analysed. The full copula-based SLD model is also applied to the Maltese, Italian, Swedish, and Danish MTPL market to test ist performance based on different market idiosyncrasies. The model framework considering the point cloud is a promising approach working well in combination with the grid-type and Bernstein copula. However, the jump pattern is not working correctly, limiting the possible developments of a single claim. Furthermore, the clustering of the data combined with the LDF surface adds too much complexity to the model focusing on the trade-off between model improvements and computing efforts. Thus, the current copula-based SLD model should not be used in practice but serves as a new and promising model framework for the development of single claims which can be developed further.    «

The accurate estimation of ultimate claims is of vital importance for reinsurance companies in respect of the pricing and risk management. Among others, models like Chain Ladder or Cape Cod are widely used in practice. Disadvantages of these models are that information of each single loss is not fully taken into account, reinsurance contract features cannot be applied correctly, and an assumption about the ultimate loss distribution has to be done. Since current single loss development (SLD) mod...    »